Curve liners

ABSTRACT

A METHOD AND APPARATUS FOR THE ALIGNMENT OF RAILROAD TRACK WHICH PROVIDES A SMOOTH TRANSITION FROM TANGENT TO CIRCULAR CURVE TRACK THROUGH A SPIRAL CURVE AND WHICH ENABLE THE APPARATUS TO BE USED IN LINING ON A SINGLE PASS THROUGH A SECTION OF TRACK. THE METHOD COMPRISES STEPS OF MEASURING PARAMETERS OF A LENGTH OF TRACK ESTABLISHING FROM THE MEASURED PARAMETERS A CURVE FORM TO WHICH THE LENGTH OF TRACK APPROXIMATES AND WHICH PROVIDES A CONSTANT RATE OF CHANGE OF CURVATURE AND ADJUSTING FOR SOME POINT IN THE LENGTH OF TRACK THE POSITION OF THE POINT TO LIE ON THE ESTABVLISHED CURVE FORM. ACCORDING TO A PREFERRED EMBODIMENT DISCLOSED THE REQUIRED CURVE FORM IS DETERMINED BY THE MEASUREMENT OF PARAMETERS DETERMINATIVE OF THE CURVATURE AT TWO POINTS IN THE LENGTH OF TRACK.

Sept.

Filed 1971 o. s. BENCSICS 3,605,625

CURVE LINERS Sept. 15, 1969 4 Sheets-Sheet l RADIOID CLOTHOID 8 Y m Q aY X0 Xb INVENTOR ODON S. BENCSICS ATTORNEYS.

20, 1971 o. s. BENCSICS 3,605,625

. CURVE LINERS Filed Sept. 15. 1969 A Sheets-Sheet 2 INVENTQR QDON S.BENCSICS ATORNEYS.

P 1971 o. s. BENCSICS 3,605,625

CURVE LINERS iled Sept. 15. 1969 4 Sheets-Sheet 5 INVENTOR ODONSBENCSICS ATTORNEYS.

United States Patent 01 Patented Sept. 20, 1971 fee US. Cl. 104-8 17Claims ABSTRACT OF THE DISCLOSURE A method and apparatus for thealignment of railroad track which provides a smooth transition fromtangent to circular curve track through a spiral curve and which enablethe apparatus to be used in lining on a single pass through a section oftrack. The method comprises steps of measuring parameters of a length oftrack, establishing from the measured parameters a curve form to whichthe length of track approximates and which provides a constant rate ofchange of curvature and adjusting for some point in the length of trackthe position of the point to lie on the established curve form.According to a preferred embodiment disclosed the required curve form isdetermined by the measurement of parameters determinative of thecurvature at two points in the length of track.

BACKGROUND OF THE INVENTION This invention relates to the lateralalignment of railroad tracks and particularly to the correction oferrors occurring in previously laid track.

Railroad track comprises three basic curve forms. These are known asstraight or tangent track, transition or spiral track, and circularcurved track. Transition track is found between stretches of tangent andcircular curved track and its function is to reduce the impact loadingon the wheels of railroad vehicles as they proceed from tangent track tocircular track or vice versa. n tangent track there is little or nolateral force on the wheels of a railroad vehicle. On circular curvedtrack there is a lateral force which is a function of the radius of thecurve, the mass of the vehicle, and the velocity of the vehicle. The useof spiral track results in a gradual increase of the lateral force fromzero on the tangent track to the maximum on entering the circular track.

With the increasing speeds of railroad vehicles, it has become importantthat the application of the lateral force should be as smooth aspossible. This requires not only that the rails of the track be freefrom lateral bumps but that the curve form of the track be as close aspossible to that required theoretically to provide the smooth transitionof forces.

Railroad track is initially laid to a given curve form. However, duringuse this curve form is lost. There are two approaches in the art to theproblem of rectifying this loss of initial curve form. One approach isto realign the track to its original curve form, working from records.The second approach is to re-align the track to provide the best curvefrom the existing state of the track. The present invention is concernedwith this secand approach. Apparatus has been developed which cansatisfactorily align both tangent track and circular curved track.However, the alignment of spiral track to a curve form which provides asmooth transition of forces still poses certain problems. Prior artapparatus has only been able to approximate spiral curves to thetheoretical best curve. For example, apparatus is known in which aspiral curve is aligned as a series of arcs of circles. In another priorart apparatus, a lining machine is first passed over a length of spiralcurve to measure variations of the curve.

A graph of these variations is prepared and an average curve is preparedfrom this graph. The lining machine then retraverses the length of trackand aligns the track to the average curve.

As will be shown hereinafter, a preferred form of curve for spiral trackis a curve which provides a constant rate of change of curvature betweenthe tangent track and the circular curved track. This form of curveprovides a smooth transition of the lateral forces on the wheels of arailroad vehicle.

SUMMARY OF THE INVENTION It is an object of the present invention toprovide a method of aligning spiral track to a curve form providing aconstant rate of change of curvature, which method is also applicable totangent and circular curved track.

It is a further object of this invention to provide such a method ofaligning railroad track which does not require the provision of externalinformation, such as the form of the track as initially laid down or thedesired form of the track.

It is a further object of the inevntion to provide such a method ofaligning track which does not require more than one pass over a lengthof the track for alignment purposes.

It is a still further object of the invention to provide apparatus forcarrying out such methods.

The present invention lies in the discovery that, from an analysis of apreferred form of spiral track, it is possible to derive at least onecontrol function which can be readily utilized in a method and apparatusfor the alignment of tangent and circular curved track as well as spiraltrack.

The control function is valid for the three basic curve forms and willnot introduce errors into those curve forms. The control function is notvalid for sections of track which comprise either part tangent and partspiral or part spiral and part circular curved track. However, theerrors introduced into such sections of track by use of the controlfunction are negligible in operating conditions of railroad track.

Essentially, the invention lies in a method of aligning railroad trackcomprising the steps of selecting a length of track; measuringparameters of that length of track; establishing from the measuredparameters a curve form to which the length of track approximates andwhich provides a constant rate of change of curvature; establishing, forsome point in the length of track, the required position of the point tolie on the curve form; and moving the track at the point towards saidposition. More particularly, the method comprises the steps of takingmeasurements, determinative of a first angle located between the tangentto a first point and a chord extending between the first point and asecond point and a second angle located between the tangent at a thirdpoint and a chord extending between the third point and a fourth point,said first, second, third, and fourth points being in said length oftrack and said first and second and said third and fourth points havingthe same straight line spacing.

The invention also provides apparatus for carrying out the method of theinvention. In general terms, said apparatus comprises means for mountingthe apparatus for movement along a track; means for measuring parametersof a selected length of the track; control means for determining fromthe measured parameters the curve form to which the length of the trackapproximates and which provides a constant rate of change of curvature;means for establishing for some point in said length of track, therequired position of said point on said curve form; and track movingmeans for moving said track at said point.

In a more particular form of the apparatus of the invention, theapparatus comprises reference line establishing means and control meansfor said reference line establishing means, said control means operableto establish a survey reference line representing a chord of a length oftrack and including means for making measurements of the parameters ofthe length of track and means for determining from the measuredparameters the curve form to which the length of track approximates andwhich provides a constant rate of change of curvature and operable toestablish a lining reference line representing a chord of said curveform and passing through a point on said curve form representing therequired position of a corresponding point of the track and means formoving said track at the corresponding point to move said point towardssaid required position.

Hereinafter there will be given an explanation of the derivation of anumber of control functions which may be used in carrying out theinvention. This derivation will include an analysis of the spiral curveform. Hereinafter there will also be described particular embodiments ofthe invention which are given by way of example.

BRIEF DESCRIPTION OF THE DRAWINGS The derivation and the embodiments ofthe invention described are given in conjunction with the accompanyingdrawings, in which:

FIG. 1 shows the geometrical relationship of two points on a transitionspiral;

FIG. 2 is a drawing illustrating the derivation of a general controlfunction;

FIG. 3 is a schematic illustration of the arrangement of elementsutilizing a first specific control function;

FIG. 4 is a schematic illustration of the arrangement of elementsutilizing a second specific control function;

FIG. 5 is a general outline drawing in plan view of apparatus embodyingthe invention;

FIG. 6 is a side elevation of the apparatus shown in FIG. 5; and

FIG. 7 is a block diagram of control means of the apparatus shown inFIGS. 4 to 6.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter there will bereference to curves and curve forms. Such terms include a straight line,a circular curve, and various other curve forms. Also, there will be useof the term constant rate of change of curvature. For the purposes ofthis specification, a straight line which has zero curvature and zerorate of change of curvature and a circle which has a constant curvatureand zero rate of change of curvature, are considered to have a constantrate of change of curvature.

It is well known, from a determination of the forces applied on a curveby a railroad vehicle that for a circular curve, the requiredsuper-elevation of the track, that is the height of the outside railabove the inside rail, can be obtained from the formula:

EP=N or where O is the radius of the curvature at a point P on thetransition curve.

4 For a smooth transition in passing from tangent track to circularcurve track along a transition curve it is necessary that the rate ofincrease of superelevation from zero to E is linear with the distancealong the transition curve, i.e.

an E L where L is the length of the transition curve from the end of thetangent track to the beginning of the circular curve track and S is thedistance from the end of the tangent track to the point P in thetransition curve.

From Equations 1 and 2 it is readily shown that:

From Equation 3 the general definition of the required transition curvetherefore becomes:

Q LR (4) L and R are constants of the particular spiral so the where ais a constant, and the curvature of the curve at a point is equal to thereciprocal of the radius at that point. Therefore, since where K is thecurvature at the point under consideration, Equation 4 can be rewrittenas:

K=aS (5) Equation K=aS is the equation of a radioid clothoid curve. Inwords, this equation states that the curvature of a point on the curveis proportional to the distance of the point from the origin of thecurve. This curve fulfills the requirement for a smooth transition offorces, ie a constant increase or decrease of forces and is a curvewhich has a constant rate of change of curvature along its length. Itwill be seen that a straight line is a special form of radioid clothoidcurve in which the constant a is zero and a circle is a special case ofthe radioid clothoid curve in which the curvature is constant.

Turning now to FIG. 1, there is shown a section of a radioid clothoidcurve commencing with zero curvature at origin 0 at the intersection ofrectangular co-ordinates X and Y and terminating in a circular curvehaving a radius of curvature R. Arbitrary points A and B are noted onthe curve.

In the following analysis: S: the arclength from the origin; L: the fulllength of the section of the radioid clothoid curve from the origin tothe circular curve; Q: the radius of curvature of the radioid clothoid;6a is the angle between the tangent to the curve at point A and the Xaxis; 7 is the angle between the chord joining A and B and the X axis; ais the angle between the chord joining A and B and the tangent at A; andA0 is the angle between tangents to the curve at A and B.

As is established above, a preferred form for a spiral curve is aradioid clothoid curve having the equation K=aS. Such a curve iscompletely defined once the c0nstant a is known.

From

K=aS and s) Thus, if it is possible to measure the curvature at twopoints a known distance apart, the curve will be completely defined.However, it is extremely difiicult to make an accurate determiation ofthe curvature of a curve at a point.

The purpose of the following analysis is to show that if a tangent isdrawn to any radioid clothoid curve at an arbitrary point A and thispoint is connected by a chord to another arbitrary point B on theclothoid, the angle between the chord and the tangent defines thecurvature of the spiral at a third related point C. Therefore, if asimilar angle is formed with points A and B at dilferent positions onthe clothoid, the angles so obtained determine the constant a of thecurve and so completely define the curve. If, therefore, the measurementof such angles is made on a length of track, the radioid clothoid curveto which that length of track approximates can be established Whetherone or more further points in that length of track lie on theestablished radioid clothoid curve for that length of track.

For the purposes of calculation, it is necessary to establish therelationship of a point on a radioid clothoid curve in terms ofrectangular X and Y co-ordinates.

Now

Therefore,

de K 3;: as

and integrating this relationship:

aS 6= afSds C where C=zero for the equation to be valid at the origin.Accordingly,

Diiferentiating results in the relationship:

s a) v5 (7) and dX=ds cos dY=ds sin 0 (8) Substituting the relationshipsof Equation 8 in Equation 7 and integrating gives the relationships:

00s 6 X= 2 I d0 0 F0 and sin 6 -r/2 Y (2a) 0 0 d0 (10) and (s 42 12There is inaccuracy due to neglecting the powers of the expressions ofsin 0 and cos 0 above 5.

From FIG. 1

tan 'y= and, therefore:

The errors involved in this derivation are due solely to approximationsof the series expansions of tan 7, sin 0, and cos 0. In the railroad artthe magnitude of 'y and 0 are such that the errors in ignoring higherpowers of these angles in the expansions are negligible.

Accordingly, it can be stated that:

Yb Ya 1 Sb0b-Sa0a =--m Xb-Xa) 3 Sb-Sa 17 From Equations 6 and 17 it canbe shown that =2 2 as use 2' (6 6 3) (18) From FIG. 1:

7=0a+a (19) and from Equation 6 2 2 8a 0a Thus S12 SaSb S112 T T3 Sb-SaSbSa 2 a since K=aS, then Sb-Sa Sb-Sa a(Sa+ 3 )K |:Sa+ and f'\ A S(AB)I: (AB)] f'\ Where =half the arclength between A and B 5121 and K ]=thecurvature at a point one-third the arelength between A and B, measuredfrom A.

Equation 22 states that the angle measured between thetangent line at apoint A and the chord If! on the radioid clothoid is equal to half thearclength between A and B multiplied by the curvature of the clothoid ata point C where C is always the distance A an 3 from A between A and B.

It can be shown by a similar development that the above relationship isalso valid when the tangent line is drawn at the point B and the angleis measured at B in which case the curvature in Equation 22 refers to apoint from B between A and B. In this latter case, the measurements arebeing taken towards the origin.

Equation 22 is also valid for circular curves. The rate of change ofcurvature of a clothoid having the relationship K =aS is as follows:

d s)-a, a constant In a circular curve the curvature is a constant, i.e.the reciprocal of the radius, therefore,

dK a? which, for the present purposes makes the circle a special case ofa radioid clothoid. Therefore:

E AS Sy-Sz for the clothoid (for the circle this expression isundefined).

Again for tangent track the rate of change of curvature is which isconstant which makes the tangent track a special case also of therelationship stated in Equation 22.

A Cubical Parabola may be represented by the equation:

y=aX (26) where, for transition curves, a is a constant and H G=Z5 whereL=length of parabola, from origin to the circular curve, measured alongthe X abscissa, i.e. the projected length of the parabolic curve, and H=the maximum offset, that is Y at the point where the parabola joins thecircle.

The curvature of a parabola is:

Where (l+9a x is always very nearly equal to 1 owing to the fact thatfor most railroad parabolic curves. Thus K is approximately equal to 6axand The expression 6a is a constant, which makes Equation 22approximately valid when applied to cubic parabolae, for

8 railroad work, where the constant a in a radioid clothoid curve hasthe value 6a in a parabolic curve.

It is to be noted that in the analyses of these clothoid and paraboliccurves a is a ditferent constant to each analysis.

Thus, it has been shown that by determining the curvature at two pointsin a length of track, by obtaining the values of the angle a at twoadjacent points on the curve, it is possible to determine not onlywhether the track is tangential, circular curved, or transition curved,but also the exact curve form to which the length of track approximatesbetween the points by which the angles a are determined and whichprovides a constant rate of change of curvature for the length of track.Tangent track is identified because K and K are zero and circular trackis identified because K =K It will thus be seen that a lining machineable to determine these angles need have no external informationprovided to it for it to be able to determine the characteristics of anylength of track on which it is placed. Since, in deriving thisrelationship, no significant approximations have been used, a liningmachine adapted to make use of the relationship can be used on tangent,circular curved, and parabolic curve track as well as spiral trackwithout introducing errors except on those lengths of track includingpart tangent and part transition, or part transition and part circular,or part tangent and part circular track. Even in these latter cases, theerrors introduced may be made insignificant for railroad work bysuitable design of apparatus.

The above analysis has been based upon the angle between the tangent ata point and the chord between that point and another point on the curve.It is to be expected that other relationships can be established forsuch curves by utilizing a difi'erent base, for example the anglebetween two chords from a given point.

It has been shown so far that the curve form. to which a length of trackapproximates and which provides a constant rate of change of curvaturecan be established by determining the curvature, by measuring a certainangle, at two points on the length of track. The next step is to find away of determining whether another point on the track in fact lies onthe required curve form and of moving that point to lie on the curveform if it is found that, in fact, the point does not lie on the curveform. Turning now to FIG. 2, there is shown a method of making thisfurther determination.

The points A, B and D on the track in FIG. 2 represent components of aliner system moving on the curve in the direction indicated by the arrowG. The points are assumed to be moving in a manner such that arclengths(Sb-Sa) and (Sd'Sa), between A and B, and between A and D, respectively,remain unchanged. This in practice cannot be completely achieved, butwith railroad ergipment it is possible to maintain constant chordlengths AB and X17 and this is suflicient for the desired accuracy ofmeasurements.

As indicated, the curve at D is in the wrong position, the lateral errorat that point being DD. This error, however, is considered small enoughto allow the assumption that ZDEZF.

In FIG. 2, a indicates the angle between the tangent to A and the chordAB and ,8 represents the angle between the chord AB and the chord BDwhere D is the point at which the track location D should be to lie on atransition curve of radioid clothoid form including the length AB.

If it can be shown that B=f(vt,a) and if means of measuring a at A andof locating a chord DB that satisfies the function B=f(u,a) areavailable, the error DD can be corrected by moving the track at D untilD is at D on DB in which case, since A ZT=A I7, W: 0.

The function p=f(a,a) is shown to exist from an analysis of Equation 22.

Considering B, BY, 5, of FIG. 2 being the angle be tween chord BD andthe tangent at B), and that Equation 22 is also valid in conditionswhere the angle between the tangent and chord is oriented toward theorigin of the spiral, then But from Equation 22 Sa= and Sb= (Kb-KG) a aa (Sb-8a) and Ka Sit- (Sd-Sa) (32) Furthermore,

m Sb-Sa=E and ,S'd-Sa=AD Therefore,

a 3Ka A A B-AD +AB+AD) (33) From Equation 22:

Sb-Sa 2a 2a. KAT 3 Sb Sa 2E Also KAT [Sa+ ]-Ka =a (Sa-l- -Sot)= AB FromEquations 34 and 35:

2a. a m Ka= AB Therefore, substituting in Equation 33:

A A A A 2 two, 3 9% 11 Equation 37 then becomes 6 f( uU- (38) To obtainthe curve constant a, two values of a, a and 11 corresponding to twopositions of the liner system on the curve, are required. Assuming achange, h, of position along the are between the two points at which ais measured, then:

Utilizing this equation in a practical machine requires that an initialmeasurement of :1 be made with the machine in a first position, and thatthe information be stored. Then the machine must be moved a knowndistance, h, along the track to a second position at which a measurementof a, a is made. At this time the stored information can be used toevaluate the equation. Similarly, for operation in subsequent positions,each measured value of 05 must be retained for computation purposes atthe next station. For simplicity, obviously h should be made a constantvalue.

It can be seen that (a oc may 'be a positive or negative quantity orzero, depending on whether the machine enters the spiral from straightor circular track or operates on a circle or tangent track. If (X2(Z1-=0then the equation is reduced to AD (1 l A B 2 which representsconditions on a circular curve. If both 0: and a, are 0, then [i=0representing conditions on a tangent track.

The practical machine, therefore, requires means for measuring the angleon between the tangent at a point A and a chord between A and B; meansfor storing the previous measurement of the angle a; means forevaluating the Equation 43 to determine the additional angle 3 which isrequired to establish a chord BD passing through a point D on thepreferred form of curve extending between A and B; and means for movingthe track in the region of the corresponding point D towards the point Duntil the point D of the track coincides with the point D of therequired curve.

In practice, the measurement of angles between various reference linesis difiicult. It is preferred that measurements of distances which aredeterminative of the various angles should be made. The measurement ofdistances from a datum to a reference line is common practice in theart. FIG. 3 illustrates a possible arrangement of components in a systemadapted to use the method described above, but making measurements ofdistance, rather than of angle. The discussion of this arrangementhereinbelow also shows how the angle measurements may be replacedbydistance measurements.

A length of track 10 has mounted thereon a number of dollies located atpredetermined distances apart. The first dolly 11 comprises a platformwhich is held in a predetermined relationship to the track 10 such thata line, R A, on the platform, is at all times tangential to the track atthe point A which lies on the track. Mounted on the platform and movablealong a line PR perpendicular to the line RA and passing through thepoint R are two radiation receivers Ru and R5. The system includes meansfor moving ROE and RB along the line PR on either side of the line R A'.The line PR is at a predetermined distance, W, from the point A. At thepoint A there is an optical pivot constituting reference line detectionmeans which may be in the form of a shadow board. Forward of theplatform in a direction of travel of the dollies is another dolly 12which incorporates track moving devices. Fixed to this dolly 12 isreference line detection means located on the track at a point D.

Ahead of the dolly 12 is another dolly 13 on which is mounted aradiation transmitter at a point B and able to transmit one or morebeams of radiation in the direction of the dollies 11 and 12. The pointB is on the track. The transmitter and receiver constitute referenceline establishing means.

Means are provided for moving receivers Rat and R 3 along the line PRand for measuring the distance R Ru and for computing a predetermineddistance R RB using the relationship B=f(a,a)

In operation of the apparatus, with the apparatus located in oneposition of the dollies 11, 12 and 13, on the track, the distance Umbetween R and Rat is measured when Ru and the points A and B are in astraight line. This first measurement of Uot, Uzx is then stored in thecomputation device. The system is moved a distance, it, along the trackand a second measurement of Ua, U01 is made when receiver Roz is in astraight line with the points A and B. The computation device thendetermines the distance Us which receiver Rf) is to be from receiver Raso that the chord between receiver RB and the transmitter at B shallintersect a radioid clothoid curve form to which the length of trackbetween A and B approximates at the point D" which is spaced a distanceAD" from A. When the computing device has made this calculation, theinformation is transmitted to the means for moving receiver RB andreceiver R is located in the required position relative to receiver Roz.

When the position of receiver RB has been determined and located, thereceiver R13 determines whether in fact the shadowboard at point D" onthe dolly 12 is in a straight line between RI? and B. If the shadowboardis not in the correct position then the lining mechanism is brought intooperation by a signal from receiver R6 to move the track towards thechord extending from receiver Re to B. In most instances the liningmechanism will have a capacity to move the track to the requiredposition where the preferred curve form between A and B and the chordbetween receiver RB and B intersects. However, the lining mechanism hasa limited force and in some instances the correction required may be solarge as to be beyond the capability of the lining machine. The functionU5 is a function of U41 and is obtained from Equation 43, i.e.

where W is the distance between A and the line PR substituting Equations44 in Equation 43 results in the device ever starts functioning.Accordingly, it will be seen that the computing device, once it has beenset up with the constants, need only be able to store the value Ua andto subtract this value from Uu multiply this value by the machineconstant, and add the resulting value to the value of U11 It will beseen that comparatively simple apparatus is required.

There are practical difficulties in maintaining the line A'R in theabove described embodiment as a tangent to the track at the point A.Accordingly, FIG. 4 shows an alternative arrangement which does notrequire that a tangent at point A be set up.

In FIG. 4 there is shown a transmitter at the point B", the opticalpivot mounted on a dolly at A, the shadowboard mounted on a dolly at Dtogether with the track moving devices, and mounted on a dolly at Ereceivers Ro' and Rfi. Receivers R0 and Rfi can move in a lineperpendicular to the track at E.

The principle of operation is very similar to the operation describedwith reference to the components of FIG. 3. The basic diiference is thatnow the datum point for measurement of the distances of the receivers isa point on the track noted as E instead of the point R on the tangent ofthe curve at the point A. FIG. 4, Se denotes the length of the are fromthe origin of the spiral to E, and the chord EA" is assumed to have alength of W.

In this case the quantity which is measured and stored is the quantityU0- which is proportional to the angle 0' which equals a-t-a, where 5 isthe angle between the chord EA" and the tangent at point A.

Accordingly the distance U5 which receiver Rfi must be located from R0to set up the chord RBB" is a function of U0 in the manner UB=G (U r).

This function can be obtained by considering 6 in relation to 0:.

From Equation 22 and using A, B, D, and W for simplicity:

sagwS'e Sa;Se] (46) Furthermore, from Equation 36:

KF MEF B and from Equation 5:

K=as (48) Combining Equations 46, 47 and 48:

bi g +W) (49) Accordingly,

W W It'F-l-W r=oz+6=(fi+1)aatherefore,

IF WE? W+E" 'T 51 Therefore,

But from Equation 42:

and therefore,

W+IE h From Equations 51 and 54:

E WZF 47 -0; W+ZF (W+ZF) h 13 but from Equation 43:

Ji l. M- Zn 323 h From Equations 43, 52 and 55, therefore: 5: It? WE L(EV -6 W+ZB" (W+It) (W+2t?) h now considering:

U H1 ZF+W and W (58) the:

A D Ii (Z77) U0'g-U0' U5Gl(Uv) W Ur 3 W Equation 59 is thus the requiredcontrol function for a system in which the datum is taken to be a pointon the track and not a point on the tangent to the track at the opticalpivot.

It will be seen that control Function (59) is in the same terms ascontrol Function (45), that is it is in the form of a constant times thesecond measurement of [L1, U0 plus a constant times the dilferencebetween the second measurement of U0, U62, and the first measurement ofUcr, U6 divided by the distance between the points at which the twomeasurements were taken.

Thus, the same equipment is required in the computing device todetermine the distance U 3.

In other words, the control Functions (43) and (59) can be written as:

Where C and C are constants; h, representing the distance moved on thetrack between the first and second positions can also be reduced to aconstant by assigning an arbitrary value to it.

FIGS. 5 and 6 illustrate a practical form of apparatus embodying thepresent invention. The apparatus illustrated combines means forlevelling railroad track and means for lining railroad track.

The apparatus comprises a main car 21 having supporting wheels 22running on a track 23. A levelling projector 24 is located ahead of thecar 21 and levelling receivers 25 are located in the body of the carbehind a shadowboard 25a. Such apparatus is known.

The radiation beam transmitting means in the present embodiment of theinvention is mounted on a dolly 26 ahead of the car 21 and takes theform of an infrared transmitter 27. The dolly 26 is held a fixeddistance ahead of the car 21 by a strut 28. Trailing the car 21 is areceiver dolly 29 which carries a survey receiver 30 and a linerreceiver 31. The dolly 29 is constrained to follow the car 21 at a fixeddistance by a strut 32. Mounted to the frame of the car 21 is a dolly 33carrying reference line detection means in the form of a shadowboard 34.The dolly 33 is constrained to travel with the car 21 but is free oflateral restraint with respect to the car 21 so that it may be heldagainst the rails of the track. Between the dolly 33 and the dolly 27are track moving means 35. These track moving means are mounted on themain frame of the car 21 and include reference line detection means inthe form of a shadowboard 36. If desired, the track moving means forlaterally moving the track can be associated with means for levellingthe track. The shadowboard 36 is so mounted that it moves laterally withlateral movement of the track. The shadowboard 36 is maintained at afixed distance from the projector 27 and the shadowboard 34 so that theelements 30, 31, 34, 36 and 27 are maintained in fixed spatialrelationship.

The receivers 30 and 31 are mounted on the end of individual shafts 37,38 and the shafts are movable laterally by motor means (not shown) inresponse to control 14 signals. A distance measuring device 39 issecured to the dolly 29 for measuring the distance moved along the trackby the apparatus.

FIG. 7 illustrates the main components in a control system for thereceivers. The diagram is shown in block form as the components arestandard equipment.

For determining the function Uo', a closed null seeking servo circuit isprovided. This is shown in the upper part of FIG. 5. The loop consistsof the receiver, Ra; an amplifier Aa; and a motor unit Me, whichcontrols a linear actuator for moving the receiver Ra along the line ERan optical pivot is provided between the receiver and the source ofradiation. This optical pivot may be, for example, a semi-transparentsheet with transparency gradually decreasing towards a pivot line. Thenull seeking servo unit functions to locate the receiver R0- in aposition in which no radiation is received. As will have been apparent,the feed-back loop of this circuit is optical.

The output from the linear actuator is abstracted from the closed loopand is converted into an analog signal by a potentiometer type rotarytransducer, To. The output, f(Ua' from transducer T is supplied to astorage circuit which holds the output for a set interval of h asdescribed above. The value of h is determined by means of a counterconnected to the reference wheel 39 running along the track. When thecounter determines that the predetermined distance h has been reached,the storage unit is actuated to feed an output function f(h, U0 to asumming circuit which also receives f(U 2), which is derived from thenull servo seeking unit at the end of the interval h. In the summingcircuit, the

function C1U0'2JFC2 W is established. The output from the summingcircuit is supplied to a closed loop servo for controlling the positionof the receiver R5. The closed loop control for receiver R5 comprises:an amplifier A5; a motor MB for controlling the linear actuator ofreceiver RB; and a feedback of function U'B through a rotary transducerTB. There is provided a subtracting unit, 4:, which relates distance Uflto the function Having now established the required position of the lineRBB, the final step is to determine whether the shadowboard D and thusthe track at D lie on the line RaB" and the required curve, or whetherto move the track and shadowboard by use of the moving mechanism mountedon the dolly fixedly carrying the shadowboard D". A system such as thatdescribed in United Kingdom Pat. No. 1,067,826 may be employed forcarrying out the determination and the track movement, as well as otherknown systems for moving a point on a track to lie on a predeterminedline.

In discussing the apparatus shown in FIGS. 5 to 7, it will be noted thatit has been suggested to use two receivers. It will be apparent that itwould be possible to use a single receiver provided that suitableswitching apparatus were incorporated in the electrical circuitry sothat the single receiver could be used initially in the surveying mode,for the determination of the angles a and a and subsequently in thelining mode. In the apparatus described it will also be necessary toprovide radiation transmitter means, reference line detection means, andreceiver means for right hand curves located on the other side of theapparatus from the location shown in the drawings. In the alternative,it will be possible to mount all the elements above the head of the carand to arrange for the elements to be movable to either the left hand orright hand side of the track.

What I claim as my invention is:

1. A method of laterally aligning railroad track comprising:

where K and K denote respectively the curvature at the two points and'(S S is the distance between the two points;

(d) establishing, for some point in the length of track, the requiredposition of the point to lie on the curve form; and

(e) moving the track at the point towards said required position.

2. A method according to claim 1 wherein, to determine the curvature(Kc) at a point (C) in the length of track, the method includes thesteps of measuring a parameter determinative of the angle (a) betweenthe tangent to the track at a first point (A) and a chord passingthrough the first point and a second point (B), where point C is onethird the distance between points A and B in the direction of B, andsolving the relationship where S is the distance between A and B.

3. A method according to claim 1 comprising measuring a distanceparameter determinative of the angle a.

4. A method according to claim 1 wherein, to establish said requiredposition of said some point (D), the method includes setting up a firstchord of the track through a point (B) at an angle 8) to a second chordextending between (B) and another point (A), where where f\ A AB and ADare, respectively, the arc lengths between A and B and A and D and isthe angle between the chord AB and the tangent at A, whereby, if saidfirst chord intersects said track at said point D, said point is at saidrequired position.

5. A method according to claim 1 including determining the curvature ata first of said points, storing information concerning the curvature atsaid first point, determining the curvature at the second of saidpoints, and finding the constant a after determining the curvature atthe second point after recalling the information on the curvature at thefirst point.

6. A method according to claim 1 including the steps of:

(a) at a first station of said points measuring first parametersdeterminative of a first angle between the chord joining the points andthe tangent at one of those points;

(b) storing said first parameters;

(c) moving said points to a second station a given distance along saidlength of track;

(d) at said second station measuring parameters of a second anglebetween the chord joining the points and the tangent at said one point.

7. A method according to claim 6 including the further steps of:

(e) establishing at said second station, a chord passing through thesecond of said two points and at an angle (,8) to the chord passingthrough the two points, where the angle is given by where (1 is saidfirst angle a is said second angle h is said given distance and C and Care constants relating to the spacing of the said two points and thesaid some point; and (f) moving the track at said some point towardssaid required position which is the location of said some point on saidchord at angle {3.

8. A method according to claim 1 wherein the parameters measured aredeterminative of a first angle located between the tangent to a firstpoint and a chord extending between the first point and a second pointand of a second angle located between the tangent at a third point and achord extending between the third point and a fourth point, said firstsecond, third and fourth points being in said length of track and saidfirst and second and said third and fourth points having the samestraight line spacmg.

9. A method according to claim 8 comprising measuring the distancesbetween said tangents and chords.

10. A method according to claim 8 comprising establishing reference linemeans through said first and second points and measuring a firstdistance between the reference line means and a fifth point on one ofsaid tangent to the first point and the track, and establishingreference line means through said third and fourth points and measuringa second distance between the reference line means and a sixth point onone of said tangent to the third point and the track, the distancebetween said first and fifth points and between said third and sixthpoints being equal.

11. A method according to claim 8 comprising the further step ofestablishing a third angle located between the chord passing through thethird and fourth points and the chord passing through said fourth pointand said required position from the relationship where ,9 is said thirdangle a is said first angle a is said second angle IE is the distancebetween said first and second and between said third and fourth points15 is the distance between said third point and said some point and L his the distance between the first and third points.

12. A method according to claim 11 including establishing reference linemeans passing through said fourth point and at said third angle to saidchord through said third and fourth points and moving the track at saidsome point towards a position in which it lies on said reference linemeans.

13. A method according to claim 10 comprising establishing referenceline means passing through said fourth point and at a third distancefrom said sixth point determined by the relationship tm=o uta+o2 whereU6 is said third distance Uot is said first distance Uu is said seconddistance h is the distance between said first and third points and C andC are constants related to the distances between various points.

1 7 14. A method according to claim 13 wherein said first, second, andthird distances are measured from said tangent to said third point andwherein and where E is the distance from the third point to said somepoint and W is the distance from said sixth point to said third point.

16. A method according to claim 13 including the step of moving saidsome point to lie on said reference line means.

17. Method of aligning railroad track comprising:

(a) locating apparatus components comprising a transmitter, receivermeans, and first and second shadowboards in a fixed spaced-apart manneralong a length of railroad track, said first shadowboard beingoperatively connected to track moving means;

(b) aligning said transmitter, receiver means and second shadowboardalong a first line;

(c) making measurements at a first position of said componentsdeterminative of the angle (04 between said first line and the tangentto the track at the second shadowboard;

(d) moving the aforementioned components along the track a distance (h)to a second position;

(e) repeating step (b);

(f) locating the receiver means in a position such that a second linejoining the transmitter and receiver means is at an angle (6) to theline joining the second shadowboard and transmitter where C and C beingconstants related to the spacing of the components, and (g) moving thetrack and the first shadowboard to said second line.

References Cited UNITED STATES PATENTS 3,165,073 1/1965 Blix et a1 104-83,314,373 4/1967 Plasser et al. 104-7 3,343,496 9/1967 Warwick 104-7ARTHUR L. LA POINT, Primary Examiner R. A. BERTSCH, Assistant Examiner

